Theorem nnssn0s 28341

Description: The positive surreal integers are a subset of the non-negative surreal integers. (Contributed by Scott Fenton, 17-Mar-2025.)

Assertion

Ref	Expression
nnssn0s	⊢ ℕs ⊆ ℕ0s

Proof of Theorem nnssn0s

Step	Hyp	Ref	Expression
1		df-nns 28336	. 2 ⊢ ℕs = (ℕ0s ∖ { 0s })
2		difss 4146	. 2 ⊢ (ℕ0s ∖ { 0s }) ⊆ ℕ0s
3	1, 2	eqsstri 4030	1 ⊢ ℕs ⊆ ℕ0s

Syntax hints:   ∖ cdif 3960   ⊆ wss 3963  {csn 4631   0_s c0s 27882  ℕ_0scnn0s 28333  ℕ_scnns 28334

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-ss 3980  df-nns 28336

This theorem is referenced by:  nnssno  28342  nnn0s  28347  nnn0sd  28348  nnsgt0  28357